Question

the graph shows the acceleration of a cyclist taking off at the beginning of a race. what was the cyclists average acceleration between 2 seconds and 5 seconds?
approximately 45 m/s²
approximately 21 m/s²
approximately 7 m/s²
approximately 12 m/s²

Explanation:

Step1: Find the speed at 2 seconds and 5 seconds

From the graph, at \(t = 2\) seconds, \(v_1\approx10\ m/s\); at \(t = 5\) seconds, \(v_2\approx31\ m/s\).

Step2: Use the formula for average acceleration

The formula for average acceleration is \(a=\frac{v_2 - v_1}{t_2 - t_1}\). Here, \(t_1 = 2\ s\), \(t_2=5\ s\), \(v_1\approx10\ m/s\), \(v_2\approx31\ m/s\). Then \(a=\frac{31 - 10}{5 - 2}=\frac{21}{3}\).

Answer:

B. Approximately \(21\ m/s^{2}\)